But, he hasn't explained why february has only 28 (or 29, depending on the year, the century and the year's divisors, :) ) days whereas all the other months have 30 or 31 days.
Every 3,7 years, if the 3rd number beginning from the right of the year is over 4, you have a month (january, august or april) that jumps 3/4 of a day and another in september, march or april (again) obtain 17 minutes more each 7 days of the month.
On these years, if the planets are aligned during fall, everything is shifted from 5 seconds to the left and 8 month to the right.
That way, we can catch the 1*10^-35,2 days we've lost during the jumping of 43 weeks for the years that end in "46".
But, if the 5th number of the year is all but a 6 and Jupiter is aligned with Sirius, it goes against the statement so we have to catch 29 days throughout the year.
That's why we have 29 days during february every 4 years (I think)...
Just because year length isnt an integer (365.249... days) due to oddsplit in continuous fraction, we have an additional day every 4 years. BUT due to evensplit in that fraction, there actually should be 8 additional days every 33 years (not 32), this mentioned by creators of gregorian calendar, so to round that up, every 100th year doesnt have additional day, and every 400th has additional day (overwrites previous)
this way we have 97 additional days per every 400 years, which is very close to mentioned 8/33 ratio
EDIT: Actually, astronoms today use EVEN WEIRDER calendar, there's no 29th feb on years, that number divides by 2000, but are if it divides by 6000. Not sure how much should we wait to an extrra day to come with that one :P